一个李代数及其相应的可积哈密顿系统

摘要

在理论上如何构造更好的可积模型，特别是无穷维哈密顿系统是可积系统研究工作的主要内容之一。本文构造了一个李代数并由此生成相应的圈代数，从而建立了一个适当的等谱问题，利用屠格式得到了一族拉克斯意义下的可积系统，根据迹恒等式得到了这个非线性可积系统的哈密顿结构。%How to construct a better integrable model in theory,especially the infinite dimensional Hamiltoni-an system,is one of the main contents of the integrable system. A Lie algebra and its loop algebra are estab-lished,from which an isospectral problem is defined. By using Tu-model,a nonlinear integrable hierarchy in the sense of Lax is obtained. Moreover,the trace identity over the corresponding loop algebra is used to fur-nish the Hamiltonian structure for the resulting nonlinear integrable system.